Negative Numbers
Understand and operate with negative numbers using the number line, and explore the concept of absolute value.
The Number Line
Negative numbers are numbers less than zero. They appear to the left of zero on the number line. We see them every day — think of temperatures below 0°C or bank overdrafts.
Numbers further left are smaller. So −5 < −2 < 0 < 3.
Adding and Subtracting Negative Numbers
Think of adding as moving right on the number line, and subtracting as moving left.
Adding Negatives
Adding a negative is the same as subtracting:
5 + (−3) = 5 − 3 = 2
−2 + (−4) = −2 − 4 = −6
Subtracting Negatives
Subtracting a negative is the same as adding:
5 − (−3) = 5 + 3 = 8
−1 − (−4) = −1 + 4 = 3
The Sign Rule to Remember
Two negatives next to each other become a positive. Like charges repel — −− becomes +, but +− stays −.
Multiplying and Dividing with Negatives
The rules for multiplication and division are based on the signs of the numbers involved.
+ × + = +
3 × 4 = 12
+ × − = −
3 × (−4) = −12
− × + = −
(−3) × 4 = −12
− × − = +
(−3) × (−4) = 12
Same signs → positive result. Different signs → negative result. Same rule applies to division.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always zero or positive.
We write absolute value using vertical bars: |−7| = 7 and |5| = 5.
|−7| = 7
7 steps from zero
|5| = 5
5 steps from zero
|0| = 0
zero steps from zero
Key Vocabulary
Negative Number
A number less than zero, written with a minus sign (e.g., −3, −7).
Integer
Any whole number, positive, negative, or zero. Examples: −4, 0, 7.
Absolute Value
The distance of a number from zero. Always positive or zero. Written as |n|.
Opposite Numbers
Numbers the same distance from zero but on opposite sides. E.g., 5 and −5.
Worked Examples
Calculate: −8 + 5
Think: Start at −8 on the number line, move 5 steps to the right.
−8 + 5 = −3
Calculate: (−4) × (−3)
Apply the sign rule: negative × negative = positive
4 × 3 = 12, so (−4) × (−3) = +12
The temperature was −3°C. It rose by 8 degrees. What is the new temperature?
New temperature = −3 + 8 = 5°C
Knowledge Check
Select the correct answer for each question.
Question 1
Calculate: −6 + 10
Question 2
Calculate: 3 − (−7)
Question 3
Calculate: (−5) × 6
Question 4
What is |−12|?
Question 5
Which is largest: −10, −3, −7, 0?
Key Concepts Summary
- ●Negative numbers are less than zero and sit to the left of zero on the number line.
- ●Adding a negative is the same as subtracting; subtracting a negative is the same as adding.
- ●Same signs in multiplication/division give a positive result; different signs give a negative result.
- ●Absolute value |n| is the distance from zero — always positive or zero.